文章基本信息

标题：Improved Fully Homomorphic Encryption over the Integers with Shorter Public Keys
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作者：Can Xiang ; Chun-ming Tang
期刊名称：International Journal of Security and Its Applications
印刷版ISSN：1738-9976
出版年度：2014
卷号：8
期号：6
页码：365-374
DOI：10.14257/ijsia.2014.8.6.31
出版社：SERSC
摘要：Fully homomorphic encryption (FHE) is a "holy grail" of cryptography. However, it is not yet adopted in practice because no known scheme is efficient. In this paper, we mainly focus on how to reduce the public key sizes in FHE. Based on Dijk et al.'s FHE scheme (DGHV) and Gentry's fully homomorhpic technology, we propose two schemes with shorter public keys by encrypting with a combination of the public key elements to replace a linear form in DGHV scheme and a quadratic form in Coron et al.'s scheme. Compared with DGHV scheme and Coron et al.'s scheme, our schemes can greatly reduce the public key sizes, which make our schemes more efficient. Furthermore, we prove the security of our schemes based on difficulties of the approximate greatest common divisor (AGCD) problem and the sparse subset sum problem.
关键词：Fully Homomorphic Encryption; Shorter Public Key Size; AGCD problem